Geodesic
Optimal grids for anisotropic problems
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 55-81
Spectral convergence of optimal grids for anisotropic problems is both numerically observed and explained. For elliptic problems, the gridding algorithm is reduced to a Stieltjes rational approximation on an interval of a line in the complex plane instead of the real axis as in the isotropic case. We show rigorously why this occurs for a semi-infinite and bounded interval. We then extend the gridding algorithm to hyperbolic problems on bounded domains. For the propagative modes, the problem is reduced to a rational approximation on an interval of the negative real semiaxis, similarly to in the isotropic case. For the wave problem we present numerical examples in 2-D anisotropic media.
Classification : 65M06, 65N06
Keywords: finite differences, dtn maps, anisotropy, spectral approximation 
@article{ETNA_2007__26__a22,
     author = {Asvadurov,  S. and Druskin,  V. and Moskow,  S.},
     title = {Optimal grids for anisotropic problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {55--81},
     year = {2007},
     volume = {26},
     zbl = {1124.65102},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a22/}
}
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AU  - Moskow,  S.
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%A Druskin,  V.
%A Moskow,  S.
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%J Electronic transactions on numerical analysis
%D 2007
%P 55-81
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%F ETNA_2007__26__a22
Asvadurov,  S.; Druskin,  V.; Moskow,  S. Optimal grids for anisotropic problems. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 55-81. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a22/